Solve for $x$ : $6x^2 - 60x + 54 = 0$
Solution: Dividing both sides by $6$ gives: $ x^2 {-10}x + {9} = 0 $ The coefficient on the $x$ term is $-10$ and the constant term is $9$ , so we need to find two numbers that add up to $-10$ and multiply to $9$ The two numbers $-1$ and $-9$ satisfy both conditions: $ {-1} + {-9} = {-10} $ $ {-1} \times {-9} = {9} $ $(x {-1}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -1) (x -9) = 0$ $x - 1 = 0$ or $x - 9 = 0$ Thus, $x = 1$ and $x = 9$ are the solutions.